## Calculus 8th Edition

$sin2y=\frac{24}{25}$
Evaluate the expression $sin2y$ Given: $sinx=\frac{1}{3}$ and $secy=\frac{5}{4}$ Since, $sin2y=2sinycosy$ ...(1) Thus, $sinx=\frac{1}{3}$ gives opp =1 , hyp = 3 and adj $=\sqrt {3^{2}-1^{2}}=2\sqrt 2$ Therefore, $cos x=\frac{2\sqrt 2}{3}$ Now, $secy=\frac{5}{4}$ gives hyp =5 , adj =4 and opp $=\sqrt {5^{2}-3^{2}}=3$ Therefore, $siny=\frac{3}{5}$ and $cosy=\frac{4}{5}$ Equation (1) becomes $sin2y=2(\frac{3}{5})(\frac{4}{5})$ Hence, $sin2y=\frac{24}{25}$